The primary objective of this study is to determine whether weekly intramuscular treatment with AVONEX (interferon beta- 1a) when compared to placebo, is effective in slowing progression of secondary progressive multiple sclerosis (MS), as determined by a composite outcome measure consisting of the Timed 25-Foot Walk, Nine-Hole (9HPT), and Paced Auditory Serial Addition Test 3 (PASAT 3).